@wikipedia
Motivation
In some specific subsurface applications which require the knowledge of subsurface temperature distributions the assumptions of constant areal geothermal profile are assumption of the Constant Areal Geothermal Temperature Profile is not valid and the problem requires a proper 3D modelling solution.
Outputs
Inputs
where
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| TVDss of the Earth's surface in a given location. In case the Earth's surface is at sea level then |
Assumptions
Equations
T_G(t, {\bf r}) = T_{GS}({\bf r}) + T_Y(t, z) + T_D(t, z) |
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G_T({\bf r}) = \frac{j_z}{\lambda_r({\bf r})} |
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\nabla T_{GS} = \lambda^{-1}\rho_e \, c_e \frac{\partial T_G}{\partial t} + \nabla \left( \lambda_e \nabla T_G \right) = q({\bf r}) |
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\cdot {\bf j}| LaTeX Math Block |
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\nabla \times {\bf j} = 0{GS}(G(t, x, y, z = z_s) = T_s |
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T_Yz) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_{en} \, A_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_{en} \, A_T}} \, \right]T_zT_D(t,z) = \delta\Big[ \lambda_e \nabla T_ |
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D, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_{en} \, D_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_D}{D_T} + (z_s -z) \sqrt {\frac{\pi}{a_{en} \, D_T}} \, \right]Big]_{z=z_{ref}} = {\bf j}(x,y, z = z_{ref}) |
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| G_T({\bf r}) = \frac{j_z({\bf r})}{\lambda_e({\bf r}) |
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| Neutral Layer |
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z_n = z_s + H_n |
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H_n = \sqrt{\frac{a_{en} \, A_T }{\pi}} \, \ln \frac{\delta T_A }{\delta T_{\rm cut}
See Also
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Geology / Geothermal Temperature Field
[ Constant Areal Geothermal Temperature Profile @model ] [ Geothermal Temperature Gradient ]
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